Presently, many of wire electric discharge machines use water as a machining fluid. In this case, a leakage current flows between a wire electrode and a workpiece, whereby electrolysis is effected. In rough machining, the leakage current does not raise any special question. In finish machining which requires control of discharge energy over a necessary range for a desired machining accuracy, however, the magnitude of the leakage current, which influences the discharge energy, arouses a question. Thus, if the energy for each cycle of electric discharge during the finish machining is large, the roughness of the machined surface of the workpiece worsens. In order to improve the surface roughness, therefore, the discharge energy must be reduced, and the peak current must be minimized. On the other hand, a predetermined amount of discharge energy must be produced to maintain stable electric discharge. Since the leakage current, however, changes as the machining conditions, including the wall thickness of the workpiece, the type of machining work, etc., vary, so it is hard to obtain a suitable amount of discharge energy under various machining conditions. If the peak current is adjusted to straight machining, for example, the leakage current increases during a corner machining process, so that a sufficient voltage for stable electric discharge cannot be obtained between the workpiece and the wire electrode.